Question: The value of $\log_{10}{579}$ is between the consecutive integers $a$ and $b$.  Find $a+b$.
Answer: We can have $\log_{10}100=2$ and $\log_{10}1000=3$.  Since $\log_{10}x$ increases as $x$ increases, we know that $\log_{10}100<\log_{10}579<\log_{10}1000$, meaning $2<\log_{10}579<3$.  Thus, the desired sum is $2+3=\boxed{5}$.